Daniel Rothstein

Correlation of adsorption isotherms of hydrocarbon gases on activated carbon

A single curve of the adsorbate volume W in the adsorbed phase versus the reduced adsorption potential φ correlates adsorption isotherms of saturated hydrocarbons of low molecular weight (viz. ethane, propane, and n-butane) at pressures from 0.034 to 10 mm Hg on Columbia 4LXC 1228 activated carbon at 25 and 30°C. This correlation is based on the Polanyi-Dubinin adsorption potential theory and the use of the Peng. Robinson equation of state to calculate thermodynamic properties. This correlation can be represented analytically by expanding the logarithm of W in terms of a quadratic polynomial in φ.

Adsorption isotherms and isosteric heats of adsorption for ethane, propane, and n-butane on polystyrene

We used a dynamic method to measure the adsorption isotherms for the gases ethane, propane, and n -butane on polystyrene at 273, 298, and 303 K. Concentrations were in the range from 500 to 10,000 ppm in a helium carrier. The isotherms can be represented by either Freundlich or Chakravarti-Dhar types. The exponent in the Freundlich isotherm increases with temperature for all three gases. The coefficient in the Freundlich isotherm increases with temperature for propane and n -butane, but decreases with increasing temperature for ethane. The isosteric heats of adsorption show a strong dependence on surface coverage. The isosteric heats were extracted in three ways: (1) from the calculated isosteres, (2) from the adsorption capacities, and (3) from the adsorption potential. The first two methods agree at all measured concentrations. Values derived from the adsorption potentials at 298 K show more variation. The characteristic curves at the three temperatures are superimposable as a single curve for each gas, but polystyrene does not show a single characteristic curve for all three gases.

Linear non-equilibrium chromatographic reactor with a first-order chemical reaction

Abstract A model is presented for a linear chromatographic reactor with a first-order reaction and three non-equilibrium processes. The following three conclusions are derived based on the Laplace transform of the reactant concentration: (1) the input-output ratio of the reactant is a function of longitudinal diffusion and interfacial diffusion in addition to the reaction rate constant; (2) moment analysis indicates that six parameters pertinent to the linear chromatographic reactor can be determined from the area ratio (or zeroth moment), and the second-order central moment as a function of flow-rate; (3) an approximation to describe the solid-phase concentration by a first-order ordinary differential equation needs a rate coefficient which depends on other parameters of the system besides the solid-phase diffusion coefficient.

Gas-solid chromatography of methane-helium mixtures: moment analysis of breakthrough curves

A moment analysis method is suggested for calculating parameters of a breakthrough curve generated from a step change of concentration of an adsorbate. The longitudinal diffusion coefficient and the solid-phase diffusion coefficient are determined from the calculated moment. A criterion is given for assessing the relative importance of the longitudinal diffusion coefficient and the solid-phase diffusion coefficient. This criterion also serves as a guide for choosing experimental parameters to determine the solid-phase diffusion coefficients.

Gas−solid chromatography of an argon−helium mixture moment analysis of a transmission curve

Abstract Transmission curves of argon in an adsorber bed packed with activated carbon were measured at 273 and 313 K. Transmission is the ratio of the adsorbate concentration at the outlet of an adsorber bed to that at the inlet. The adsorption isotherm, as determined from a mass-balance equation, was found to be linear. The method of moments was used to extract two kinetic parameters ( viz., the longitudinal diffusion coefficient and the solid-phase diffusion coefficient) at these two temperatures. Also the dimensionless adsorption capacity was determined at both temperatures. The activation energy of diffusion in the solid phase is found to be close to the isosteric heat of adsorption.

Correlation of heterogeneity parameters for adsorption of single gases and gas mixtures on solids

Abstract Adsorption isotherms of single hydrocarbons on polystyrene and activated carbon adsorbents are described by an equation, which is an extension of Langmuir isotherm for a quasi-Gaussian energy distribution function. A simple analog of this equation is used to represent adsorption of binary hydrocarbon mixtures on these adsorbents. It is shown that this equation gives a good representation of mixed-gas adsorption isotherms; moreover, the heterogeneity parameters, including the dispersion of the adsorption energy, extracted from mixed-gas isotherms correlate with those obtained from suitable single-gas isotherms. Some suggestions concerning prediction of mixed-gas adsorption equilibria are presented.

Adsorption of n-butane and 1,3-butadiene on cross-linked polystyrene

Abstract Adsorption isotherms of n -butane and 1,3-butadiene and their mixtures on cross-linked polystyrene at 25°C were measured by the frontal analysis method. Single-component isotherms appear to be of the Freundlich type. A binary Freundlich isotherm is adopted for discussing binary data and a method for calculating binary parameters is presented. Another binary Freundlich isotherm, which fails to agree with our data, was examined also.

Pressure swing adsorption for a system with a langmuir-freundlich isotherm

Abstract Expressions for the enrichment factor, the critical recycle ratio, and the extent of recovery are discussed for a pressure swing adsorption system with a Langmuir—Freundlich isotherm. The enrichment factor is defined as the ratio of the mole fraction of the adsorbate gas in the low-pressure product stream to that in the high-pressure feed stream, the critical recycle ratio is defined as the ratio of the number of moles of the purge gas to the total number of moles of high-pressure product gas, and the extent of recovery is defined as the ratio of the net amount of the carrier gas in the product stream to the total amount of the carrier gas that enters the bed during a cycle. Effects of the non-linear isotherm parameters on these quantities are discussed. It is shown that the enrichment factor increases with increasing adsorbent heterogeneity, whereas the extent of recovery and the critical recycle ratio depend only slightly on the heterogeneity parameter.

Pressure swing adsorption for a system with a Freundlich isotherm

An analytical expression is obtained for the equilibrium relationship between the enrichment factor of the product stream and the ratio of the pressure in the feed stream to that in the product stream for a pressure-swing-adsorption system with a Freundlich isotherm. The enrichment factor is the ratio of the mole fraction of the adsorbate in the product gas stream to that in the feed gas stream. The enrichment factor increases with increasing pressure ratio in a manner similar to that for a system with a linear isotherm. The nonlinearity of the Freundlich isotherm does not result in a significant reduction in the enrichment factor.

Adsorption of binary mixtures of ethane and acetylene on activated carbon

Abstract Dynamic measurements of the adsorption of binary mixtures of ethane and acetylene (and also of each gas alone) in a helium carrier gas were made on an (Columbia 4LXC 12/28) activated carbon adsorber bed at 25°C. The adsorption capacities of the activated carbon for the pure gases and for each component in the mixtures are extracted from the transmission curves by the use of a mass balance equation. Transmission is the ratio of the concentration at the outlet of the adsorber bed to that at the inlet. The adsorption isotherms for pure ethane and acetylene can be represented by a modified Langmuir isotherm known as the Chakravarti-Dhar isotherm at gas concentrations up to at least 4.2 ± 10−7 mol/cm3 (viz., 7.8 mmHg). The gas-adsorbate equilibrium composition and the adsorption capacity of each component in the binary mixture of ethane and acetylene are estimated from the corresponding single-component isotherms by applying ideal adsorbed solution theory (IAST). The fact that the estimated values of ...